The number of critical points of the function f(x)= 2 3 x^3 - x 2 + _ 1 ^ x ( 1 2 + 1…

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

The number of critical points of the function

f(x)=\frac{2}{3}\sqrt{x^3}-\frac{x}{2}+\int_{1}^{x}\left(\frac{1}{2}+\frac{1}{2}\cos2t-\sqrt{t}\right)dt

that lie in the interval

[-2\pi,2\pi]

is _____.